Practice Parallelism in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Lines in the same plane that never intersect because they maintain a constant distance from each other.

Railroad tracks—they stay exactly the same distance apart and never meet, no matter how far they extend.

Showing a random 20 of 50 problems.

Example 1

easy
What stays constant between two parallel lines?

Example 2

easy
Do parallel lines ever intersect?

Example 3

easy
What is the slope of any line parallel to y=−4x+9y = -4x + 9?

Example 4

medium
A line passes through (−1,4)(-1, 4) and is parallel to 5x+y=95x + y = 9. Write its equation in slope-intercept form.

Example 5

easy
Two lines have slopes 3 and 3. Are they parallel?

Example 6

challenge
A transversal makes alternate interior angles of (2x+10)∘(2x + 10)^\circ and (3x−20)∘(3x - 20)^\circ with two lines. For the lines to be parallel, find xx.

Example 7

hard
A line parallel to y=−34x+2y = -\tfrac{3}{4}x + 2 passes through the point of intersection of x+y=5x + y = 5 and x−y=1x - y = 1. Find its equation.

Example 8

medium
A transversal crosses two parallel lines making co-interior (same-side interior) angles of xx and 110∘110^\circ. Find xx.

Example 9

easy
Fill in the blank: Two distinct parallel lines have ___ points in common.

Example 10

hard
In △ABC\triangle ABC, DD is on ABAB with AD=3AD = 3, DB=6DB = 6, and EE is on ACAC such that DE∥BCDE \parallel BC. If AC=15AC = 15, find AEAE.

Example 11

medium
Write the equation of the line through (0,5)(0, 5) parallel to y=3x−2y = 3x - 2.

Example 12

easy
Are the lines y=12x+3y = \tfrac{1}{2}x + 3 and y=12x−7y = \tfrac{1}{2}x - 7 parallel?

Example 13

medium
A parallelogram has vertices A(0,0)A(0, 0), B(6,0)B(6, 0), D(2,3)D(2, 3). Find CC so that ABCDABCD is a parallelogram.

Example 14

medium
Two lines are each parallel to a third line. Are the two lines parallel to each other?

Example 15

hard
Quadrilateral WXYZWXYZ has W(0,0)W(0, 0), X(7,2)X(7, 2), Y(9,8)Y(9, 8), Z(2,6)Z(2, 6). Is it a parallelogram?

Example 16

easy
Line A has slope 4. For a line to be parallel to A, what must its slope be?

Example 17

medium
Find the slope of a line parallel to the line through (1,2)(1, 2) and (5,10)(5, 10).

Example 18

hard
Given three lines, what is the maximum number of pairs that can all be mutually parallel?

Example 19

challenge
Find the distance between the parallel lines y=2x+1y = 2x + 1 and y=2x+6y = 2x + 6.

Example 20

medium
Why can't you trust that two lines drawn 'looking parallel' in a diagram are actually parallel?
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